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lean4/tests/elab/bool_simp.lean
Garmelon 08eb78a5b2 chore: switch to new test/bench suite (#12590) 
This PR sets up the new integrated test/bench suite. It then migrates
all benchmarks and some related tests to the new suite. There's also
some documentation and some linting.

For now, a lot of the old tests are left alone so this PR doesn't become
even larger than it already is. Eventually, all tests should be migrated
to the new suite though so there isn't a confusing mix of two systems.
2026-02-25 13:51:53 +00:00

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variable (p q : Prop)
variable (b c d : Bool)
variable (u v w : Prop) [Decidable u] [Decidable v] [Decidable w]
-- Specific regressions found when introducing Boolean normalization
#check_simp (b != !c) = false ~> b ≠ c
#check_simp ¬(u → v ∨ w) ~> u ∧ ¬v ∧ ¬w
#check_simp decide (u ∧ (v → False)) ~> decide u && !decide v
#check_simp decide (cond true b c = true) ~> b
#check_simp decide (ite u b c = true) ~> ite u b c
#check_simp true ≠ (b || c) ~> b = false ∧ c = false
#check_simp ¬((!b = false) ∧ (c = false)) ~> b = true → c = true
#check_simp (((!b) && c) ≠ false) ~> b = false ∧ c = true
#check_simp (cond b false c ≠ false) ~> b = false ∧ c
#check_simp (b && c) = false ~> b → c = false
#check_simp (b && c) ≠ false ~> b ∧ c
#check_simp decide (u → False) ~> !decide u
#check_simp decide (¬u) ~> !decide u
#check_simp (b = true) ≠ (c = false) ~> b = c
#check_simp (b != c) != (false != d) ~> b != (c != d)
#check_simp (b == false) ≠ (c != d) ~> b = (c != d)
#check_simp (b = true) ≠ (c = false) ~> b = c
#check_simp ¬b = !c ~> b = c
#check_simp (b == c) = false ~> ¬(b = c)
#check_simp (true ≠ if u then b else c) ~> (if u then b = false else c = false)
#check_simp (u ∧ v → False) ~> u → v → False
#check_simp (u = (v ≠ w)) ~> (u ↔ ¬(v ↔ w))
#check_simp ((b = false) = (c = false)) ~> b = c
#check_simp True ≠ (c = false) ~> c = true
#check_simp u ∧ u ∧ v ~> u ∧ v
#check_simp b || (b || c) ~> b || c
#check_simp ((b ≠ c) : Bool) ~> !(decide (b = c))
#check_simp ((u ≠ v) : Bool) ~> !((u : Bool) == (v : Bool))
#check_simp decide (u → False) ~> !(decide u)
#check_simp decide (¬u) ~> !u
-- Specific regressions done
-- Round trip isomorphisms
#check_simp (decide (b : Prop)) ~> b
#check_simp ((u : Bool) : Prop) ~> u
/- # not -/
variable [Decidable u]
-- Ground
#check_simp (¬True) ~> False
#check_simp (¬true) ~> False
#check_simp (!True) ~> false
#check_simp (!true) ~> false
#check_simp (¬False) ~> True
#check_simp (!False) ~> true
#check_simp (¬false) ~> True
#check_simp (!false) ~> true
/- # Coercions and not -/
#check_simp ¬p !~>
#check_simp !b !~>
#check_simp (¬u : Prop) !~>
#check_simp (¬u : Bool) ~> !u
#check_simp (!u : Prop) ~> ¬u
#check_simp (!u : Bool) !~>
#check_simp (¬b : Prop) ~> b = false
#check_simp (¬b : Bool) ~> !b
#check_simp (!b : Prop) ~> b = false
#check_simp (!b : Bool) !~>
#check_simp (¬¬u) ~> u
/- # and -/
-- Validate coercions
#check_simp (u ∧ v : Prop) !~>
#check_simp (u ∧ v : Bool) ~> u && v
#check_simp (u && v : Prop) ~> u ∧ v
#check_simp (u && v : Bool) !~>
#check_simp (b ∧ c : Prop) !~>
#check_simp (b ∧ c : Bool) ~> b && c
#check_simp (b && c : Prop) ~> b ∧ c
#check_simp (b && c : Bool) !~>
-- Partial evaluation
#check_simp (True ∧ v : Prop) ~> v
#check_simp (True ∧ v : Bool) ~> (v : Bool)
#check_simp (True && v : Prop) ~> v
#check_simp (True && v : Bool) ~> (v : Bool)
#check_simp (true ∧ c : Prop) ~> (c : Prop)
#check_simp (true ∧ c : Bool) ~> c
#check_simp (true && c : Prop) ~> (c : Prop)
#check_simp (true && c : Bool) ~> c
#check_simp (u ∧ True : Prop) ~> u
#check_simp (u ∧ True : Bool) ~> (u : Bool)
#check_simp (u && True : Prop) ~> u
#check_simp (u && True : Bool) ~> (u : Bool)
#check_simp (b ∧ true : Prop) ~> (b : Prop)
#check_simp (b ∧ true : Bool) ~> b
#check_simp (b && true : Prop) ~> (b : Prop)
#check_simp (b && true : Bool) ~> b
#check_simp (False ∧ v : Prop) ~> False
#check_simp (False ∧ v : Bool) ~> false
#check_simp (False && v : Prop) ~> False
#check_simp (False && v : Bool) ~> false
#check_simp (false ∧ c : Prop) ~> False
#check_simp (false ∧ c : Bool) ~> false
#check_simp (false && c : Prop) ~> False
#check_simp (false && c : Bool) ~> false
#check_simp (u ∧ False : Prop) ~> False
#check_simp (u ∧ False : Bool) ~> false
#check_simp (u && False : Prop) ~> False
#check_simp (u && False : Bool) ~> false
#check_simp (b ∧ false : Prop) ~> False
#check_simp (b ∧ false : Bool) ~> false
#check_simp (b && false : Prop) ~> False
#check_simp (b && false : Bool) ~> false
-- Idempotence
#check_simp (u ∧ u) ~> u
#check_simp (u && u) ~> (u : Bool)
#check_simp (b ∧ b) ~> (b : Prop)
#check_simp (b && b) ~> b
-- Cancellation
#check_simp (u ∧ ¬u) ~> False
#check_simp (¬u ∧ u) ~> False
#check_simp (b && ¬b) ~> false
#check_simp (¬b && b) ~> false
-- Check we swap operators, but do apply deMorgan etc
#check_simp ¬(u ∧ v) ~> u → ¬v
#check_simp decide (¬(u ∧ v)) ~> !u || !v
#check_simp !(u ∧ v) ~> !u || !v
#check_simp ¬(b ∧ c) ~> b → c = false
#check_simp !(b ∧ c) ~> !b || !c
#check_simp ¬(u && v) ~> u → ¬ v
#check_simp ¬(b && c) ~> b = true → c = false
#check_simp !(u && v) ~> !u || !v
#check_simp !(b && c) ~> !b || !c
#check_simp ¬u ∧ ¬v !~>
#check_simp ¬b ∧ ¬c ~> ((b = false) ∧ (c = false))
#check_simp ¬u && ¬v ~> (!u && !v)
#check_simp ¬b && ¬c ~> (!b && !c)
-- Some ternary test cases
#check_simp (u ∧ (v ∧ w) : Prop) !~>
#check_simp (u ∧ (v ∧ w) : Bool) ~> (u && (v && w))
#check_simp ((u ∧ v) ∧ w : Prop) !~>
#check_simp ((u ∧ v) ∧ w : Bool) ~> ((u && v) && w)
#check_simp (b && (c && d) : Prop) ~> (b ∧ c ∧ d)
#check_simp (b && (c && d) : Bool) !~>
#check_simp ((b && c) && d : Prop) ~> ((b ∧ c) ∧ d)
#check_simp ((b && c) && d : Bool) !~>
/- # or -/
-- Validate coercions
#check_simp p ∨ q !~>
#check_simp q ∨ p !~>
#check_simp (u ∨ v : Prop) !~>
#check_simp (u ∨ v : Bool) ~> u || v
#check_simp (u || v : Prop) ~> u ∨ v
#check_simp (u || v : Bool) !~>
#check_simp (b ∨ c : Prop) !~>
#check_simp (b ∨ c : Bool) ~> b || c
#check_simp (b || c : Prop) ~> b ∨ c
#check_simp (b || c : Bool) !~>
-- Partial evaluation
#check_simp (True ∨ v : Prop) ~> True
#check_simp (True ∨ v : Bool) ~> true
#check_simp (True || v : Prop) ~> True
#check_simp (True || v : Bool) ~> true
#check_simp (true ∨ c : Prop) ~> True
#check_simp (true ∨ c : Bool) ~> true
#check_simp (true || c : Prop) ~> True
#check_simp (true || c : Bool) ~> true
#check_simp (u ∨ True : Prop) ~> True
#check_simp (u ∨ True : Bool) ~> true
#check_simp (u || True : Prop) ~> True
#check_simp (u || True : Bool) ~> true
#check_simp (b ∨ true : Prop) ~> True
#check_simp (b ∨ true : Bool) ~> true
#check_simp (b || true : Prop) ~> True
#check_simp (b || true : Bool) ~> true
#check_simp (False ∨ v : Prop) ~> v
#check_simp (False ∨ v : Bool) ~> (v : Bool)
#check_simp (False || v : Prop) ~> v
#check_simp (False || v : Bool) ~> (v : Bool)
#check_simp (false ∨ c : Prop) ~> (c : Prop)
#check_simp (false ∨ c : Bool) ~> c
#check_simp (false || c : Prop) ~> (c : Prop)
#check_simp (false || c : Bool) ~> c
#check_simp (u ∨ False : Prop) ~> u
#check_simp (u ∨ False : Bool) ~> (u : Bool)
#check_simp (u || False : Prop) ~> u
#check_simp (u || False : Bool) ~> (u : Bool)
#check_simp (b ∨ false : Prop) ~> (b : Prop)
#check_simp (b ∨ false : Bool) ~> b
#check_simp (b || false : Prop) ~> (b : Prop)
#check_simp (b || false : Bool) ~> b
-- Idempotence
#check_simp (u ∨ u) ~> u
#check_simp (u || u) ~> (u : Bool)
#check_simp (b ∨ b) ~> (b : Prop)
#check_simp (b || b) ~> b
-- Complement
-- Note. We may want to revisit this.
-- Decidable excluded middle currently does not simplify.
#check_simp ( u ∨ ¬u) !~>
#check_simp (¬u ∨ u) !~>
#check_simp ( b || ¬b) ~> true
#check_simp (¬b || b) ~> true
-- Check we swap operators, but do apply deMorgan etc
#check_simp ¬(u ∨ v) ~> ¬u ∧ ¬v
#check_simp !(u ∨ v) ~> !u && !v
#check_simp ¬(b ∨ c) ~> b = false ∧ c =false
#check_simp !(b ∨ c) ~> !b && !c
#check_simp ¬(u || v) ~> ¬u ∧ ¬v
#check_simp ¬(b || c) ~> b = false ∧ c = false
#check_simp !(u || v) ~> !u && !v
#check_simp !(b || c) ~> !b && !c
#check_simp ¬u ∨ ¬v !~>
#check_simp (¬b) ∨ (¬c) ~> b = false ∨ c = false
#check_simp ¬u || ¬v ~> (!u || !v)
#check_simp ¬b || ¬c ~> (!b || !c)
-- Some ternary test cases
#check_simp (u ∨ (v ∨ w) : Prop) !~>
#check_simp (u ∨ (v ∨ w) : Bool) ~> (u || (v || w))
#check_simp ((u ∨ v) ∨ w : Prop) !~>
#check_simp ((u ∨ v) ∨ w : Bool) ~> ((u || v) || w)
#check_simp (b || (c || d) : Prop) ~> (b ∨ c ∨ d)
#check_simp (b || (c || d) : Bool) !~>
#check_simp ((b || c) || d : Prop) ~> ((b ∨ c) ∨ d)
#check_simp ((b || c) || d : Bool) !~>
/- # and/or -/
-- We don't currently do automatic simplification across and/or/not
-- This tests for non-unexpected reductions.
#check_simp p ∧ (p ∨ q) !~>
#check_simp (p ∨ q) ∧ p !~>
#check_simp u ∧ (v ∨ w) !~>
#check_simp u ∨ (v ∧ w) !~>
#check_simp (v ∨ w) ∧ u !~>
#check_simp (v ∧ w) ∨ u !~>
#check_simp b && (c || d) !~>
#check_simp b || (c && d) !~>
#check_simp (c || d) && b !~>
#check_simp (c && d) || b !~>
/- # implication -/
#check_simp (b → c) !~>
#check_simp (u → v) !~>
#check_simp p → q !~>
#check_simp decide (u → ¬v) ~> !u || !v
/- # iff -/
#check_simp (u = v : Prop) ~> u ↔ v
#check_simp (u = v : Bool) ~> u == v
#check_simp (u ↔ v : Prop) !~>
#check_simp (u ↔ v : Bool) ~> u == v
#check_simp (u == v : Prop) ~> u ↔ v
#check_simp (u == v : Bool) !~>
#check_simp (b = c : Prop) !~>
#check_simp (b = c : Bool) !~>
#check_simp (b ↔ c : Prop) ~> b = c
#check_simp (b ↔ c : Bool) ~> decide (b = c)
#check_simp (b == c : Prop) ~> b = c
#check_simp (b == c : Bool) !~>
-- Partial evaluation
#check_simp (True = v : Prop) ~> v
#check_simp (True = v : Bool) ~> (v : Bool)
#check_simp (True ↔ v : Prop) ~> v
#check_simp (True ↔ v : Bool) ~> (v : Bool)
#check_simp (True == v : Prop) ~> v
#check_simp (True == v : Bool) ~> (v : Bool)
#check_simp (true = c : Prop) ~> c = true
#check_simp (true = c : Bool) ~> c
#check_simp (true ↔ c : Prop) ~> c = true
#check_simp (true ↔ c : Bool) ~> c
#check_simp (true == c : Prop) ~> (c : Prop)
#check_simp (true == c : Bool) ~> c
#check_simp (v = True : Prop) ~> v
#check_simp (v = True : Bool) ~> (v : Bool)
#check_simp (v ↔ True : Prop) ~> v
#check_simp (v ↔ True : Bool) ~> (v : Bool)
#check_simp (v == True : Prop) ~> v
#check_simp (v == True : Bool) ~> (v : Bool)
#check_simp (c = true : Prop) !~>
#check_simp (c = true : Bool) ~> c
#check_simp (c ↔ true : Prop) ~> c = true
#check_simp (c ↔ true : Bool) ~> c
#check_simp (c == true : Prop) ~> c = true
#check_simp (c == true : Bool) ~> c
#check_simp (True = v : Prop) ~> v
#check_simp (True = v : Bool) ~> (v : Bool)
#check_simp (True ↔ v : Prop) ~> v
#check_simp (True ↔ v : Bool) ~> (v : Bool)
#check_simp (True == v : Prop) ~> v
#check_simp (True == v : Bool) ~> (v : Bool)
#check_simp (true = c : Prop) ~> c = true
#check_simp (true = c : Bool) ~> c
#check_simp (true ↔ c : Prop) ~> c = true
#check_simp (true ↔ c : Bool) ~> c
#check_simp (true == c : Prop) ~> (c : Prop)
#check_simp (true == c : Bool) ~> c
#check_simp (v = False : Prop) ~> ¬v
#check_simp (v = False : Bool) ~> !v
#check_simp (v ↔ False : Prop) ~> ¬v
#check_simp (v ↔ False : Bool) ~> !v
#check_simp (v == False : Prop) ~> ¬v
#check_simp (v == False : Bool) ~> !v
#check_simp (c = false : Prop) !~>
#check_simp (c = false : Bool) ~> !c
#check_simp (c ↔ false : Prop) ~> c = false
#check_simp (c ↔ false : Bool) ~> !c
#check_simp (c == false : Prop) ~> c = false
#check_simp (c == false : Bool) ~> !c
#check_simp (False = v : Prop) ~> ¬v
#check_simp (False = v : Bool) ~> !v
#check_simp (False ↔ v : Prop) ~> ¬v
#check_simp (False ↔ v : Bool) ~> !v
#check_simp (False == v : Prop) ~> ¬v
#check_simp (False == v : Bool) ~> !v
#check_simp (false = c : Prop) ~> c = false
#check_simp (false = c : Bool) ~> !c
#check_simp (false ↔ c : Prop) ~> c = false
#check_simp (false ↔ c : Bool) ~> !c
#check_simp (false == c : Prop) ~> c = false
#check_simp (false == c : Bool) ~> !c
-- Ternary (expand these)
#check_simp (u == (v = w)) ~> u == (v == w)
#check_simp (u == (v == w)) !~>
/- # bne -/
#check_simp p ≠ q ~> ¬(p ↔ q)
#check_simp (b != c : Bool) !~>
#check_simp ¬(p = q) ~> ¬(p ↔ q)
#check_simp b ≠ c ~> b ≠ c
#check_simp ¬(b = c) !~>
#check_simp ¬(b ↔ c) ~> ¬(b = c)
#check_simp (b != c : Prop) ~> b ≠ c
#check_simp u ≠ v ~> ¬(u ↔ v)
#check_simp ¬(u = v) ~> ¬(u ↔ v)
#check_simp ¬(u ↔ v) !~>
#check_simp ((u:Bool) != v : Bool) !~>
#check_simp ((u:Bool) != v : Prop) ~> ¬(u ↔ v)
/- # equality and and/or interactions -/
#check_simp (u == (v ∨ w)) ~> u == (v || w)
#check_simp (u == (v || w)) !~>
#check_simp ((u ∧ v) == w) ~> (u && v) == w
/- # ite/cond -/
#check_simp if b then c else d !~>
#check_simp if b then p else q !~>
#check_simp if u then p else q !~>
#check_simp if u then b else c !~>
#check_simp if u then u else q ~> ¬u → q
#check_simp if u then q else u ~> u ∧ q
#check_simp if u then q else q ~> q
#check_simp cond b c d !~>
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